The subject of this book is a new direction in the field ofprobability theory and mathematical statistics which can becalled "stability theory": it deals with evaluating theeffects of perturbing initial probabilistic models andembraces quite varied subtopics: limit theorems, queueingmodels, statistical inference, probability metrics, etc. Thecontributions are original research articles developing newideas and methods of stability analysis.

Characterizations of the pareto distribution based on order statistics.- Some characterizations of the exponential distribution based on the service time properties of an unreliable server.- On the distribution of the Wilcoxon Rank-Sum statistic.- On different stability-concepts for probabilities on groups.- Functional limit theorems for random walks on one-dimensional hypergroups.- Stabilities and instabilities in population dynamics.- Some properties of random variables which are stable with respect to the random sample size.- Two-side estimates of geometric convolutions.- A stochastic model of radiation carcinogenesis.- Limit theorems for random sums of independent random variables.- On regularly varying multivalued functions.- A comparison theorem for queueing system with non-identical channels.- On an intrinsic bias measure.- Characterization of exponential distributions by conditional moments.- The functional limit theorem on nilpotent lie group.- On wide-sense regeneration.- Some properties of the median of the stable distributions close to the symmetric ones.- Regeneration, stationarity and simulation.- Multivariate infinitely divisible distributions with the gaussian second order conditional structure.- On the convergence of random symmetric polynomials.- Stability of characterization by record properties.- A berry - esseen bound for multivariate l-estimates with explicit dependence on dimension.- On the ergodicity condition of random walks with a periodic control sequence.- Some limit problem for dependent random variables.